A martingale characterization of the set-indexed Brownian motion

B. Gail Ivanoff, Ely Merzbach

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

We characterize a Brownian motion indexed by a semilattice of sets, using the theory of set-indexed martingales: a square integrable continuous set-indexed strong martingale is a Brownian motion if and only if its compensator is deterministic and continuous.

Original languageEnglish
Pages (from-to)903-913
Number of pages11
JournalJournal of Theoretical Probability
Volume9
Issue number4
DOIs
StatePublished - Oct 1996

Keywords

  • Compensator
  • Lattice
  • Set-indexed Brownian motion
  • Strong martingale

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